Multi-label Classification with non-binary outputs
Technically, you're not really doing classification The outputs you have are not labels, they are real values. So I've got two (possible!) solutions, and you'll have to test them out for yourself:

Solution 1

Because each output is actually a numerical value, you can normalize them just like you would normalize all other numerical values. So you choose a maximum value that you would expect for the labels (you can also do this per label), and divide the actual value by that value to normalize it.

So if you don't expect more than 10 of the same amino acids in each peptide sequence, then you divide all amounts by 10:

0 becomes 0.0
1 becomes 0.1
2 becomes 0.2
3 becomes 0.3
etc.


Solution 2

This is more complex, but if you'd give it a try it would surely work. This solution requires recurrent networks. Just like LSTM networks are good for character-by-character text prediction, they will work for your 'peptide sequence language' as well.

This solution also allows an output sequence of any length.

How it works? You have a network with óne output (m/z), and 22 outputs (one-hot encoded amino acids) + 1 more, when this output has the highest value it tells you that the sequence has finished. 

You keep on inputting the same value of m/z, until your network tells that the sequence has finished. The network will output different letters every activation based on the previous outputs (the LSTM model has some kind of memory).

This solution is kind of hard to explain, but if you provide me with a small list of peptide sequences (not too long, and not too much), then i'll make a working online example of you.



As promised, I made simple implementation of solution 2. However, I think you should go for solution 1 anyways. I didn't have any real data, so my model is basically overfitting, but it basically works: https://jsfiddle.net/ovpkL2xx/2/ (might take some time to run)

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